v1-Periodic 2-exponents of SU(2^e) and SU(2^e + 1)

TL;DR

This paper precisely determines the largest v1-periodic homotopy groups of SU(2^e) and SU(2^e + 1), providing new insights into their homotopy structures using advanced combinatorial divisibility results.

Contribution

It offers exact calculations of v1-periodic homotopy groups for specific special unitary groups, extending understanding of their homotopy properties.

Findings

Largest v1-periodic homotopy groups of SU(2^e) and SU(2^e + 1) determined

New results on the actual homotopy groups of these spaces

Utilizes binomial coefficient divisibility results from a companion paper

Abstract

We determine precisely the largest v1-periodic homotopy groups of SU(2^e) and SU(2^e + 1). This gives new results about the largest actual homotopy groups of these spaces. Our proof relies on results about 2-divisibility of restricted sums of binomial coefficients times powers proved by the author in a companion paper.